Aircraft: CHANCELLOR 414A / C414
Phase of flight: Climb
Anomaly: Aircraft Equipment Problem Critical; Flight Deck / Cabin / Aircraft Event Smoke / Fire / Fumes / Odor; Inflight Event / Encounter Wake Vortex Encounter; Inflight Event / Encounter Weather / Turbulence

I was the PF/Receiving training on this flight. After takeoff I experienced a sudden small roll to the left. I was hand flying and visually corrected back to wings level. We would penetrate clouds soon so I selected both pitot heat switches to the ON position. The right pitot heat circuit breaker immediately blew. An attempted reset was unsuccessful. We were assigned a right turn to a 095 (I believe) heading. After turning to the assigned heading; I experienced another small but sudden left roll. I then switched on the auto pilot in HDG mode as we continued to climb. I then noticed the airspeed seemed to be fluctuating. Not wanting to enter the clouds with system malfunctions; I started a turn to a right downwind leg while discontinuing the climb. I was reminded by the PNF/Instructor that the auto pilot was ON and I was inadvertently fighting it. As this was being discussed; I felt another small roll. I shut off the auto pilot and informed the PNF/Instructor that I was having control problems and did not wish to continue. After the auto pilot was turned OFF; we still experienced intermittent rolls. The PNF then informed the tower that we wanted to return to [departure airport]. They started vectors for sequencing to follow other aircraft so I informed the PNF that the control issues were still continuing. He then told ATC that we requested immediate landing clearance. Airspeed was fluctuating wildly and I then found out that the copilot airspeed was also fluctuating. While selecting the landing gear to the DOWN position; I noticed that all three gear lights were already on. The gear had apparently never retracted and I had not yet noticed due to the other distractions. We landed without further incident. We noticed the emergency trucks proceeding along the airport perimeter. After receiving taxi clearance and heading along the parallel; we informed Ground that we seemed to be fine now and they could call off the trucks. Approximately 1000 feet from the FBO; we noticed white smoke billowing from the defrost ducts. We then informed Ground to send the CFR vehicles to the ramp; and that we had smoke in the cockpit. We parked away from the buildings by the grass; powered down and evacuated. After assuring the passengers were safe and well clear; I opened the left nose baggage door and white smoke billowed out. The fire crew inspected the aircraft and found no fire but did notice scorch marks and minor smoke on the bulkhead baggage compartment vertical wall. At the time of this writing; no further evaluation has been done to determine the exact cause of the seemingly unrelated events. I was the PM/Instructor for the flight. After departure; pitot heat was selected on for both pitot tubes by the PF. The right pitot heat CB popped. Shortly thereafter; the Pilot Flying this aircraft reported an odd control malfunction in the roll axis. I noticed that he appeared to be fighting the autopilot; and asked if he was aware it was on. He was; but turned it off. The roll malfunction (jerk of the yoke) continued intermittently. We remained below the clouds and told ATC we wanted to return to [the departure airport]. They started vectoring us for a long final; and the PF stated it was getting worse. I immediately [notified ATC] and told the PF to turn toward the airport. We landed without incident. After receiving a taxi clearance; we headed toward the FBO. About 500-1000 feet from the ramp; white smoke started to billow from the defrost ducts. I told the PF to head to the ramp immediately. I called ATC and told them to send the CFR vehicles to the ramp; and that we had smoke in the cockpit; and was depowering the aircraft (electrically). CFR met us and I asked them to use their IR camera to inspect the nose of the aircraft to verify no fire exists in the closed compartments.After the previous inbound flight; the CB popped for the cabin fan. We then found the heater inop. We discussed the issue with our normal maintenance and all agreed the aircraft would be safe to fly with the heater and cabin fan inop for the relatively short flight home. Both were placarded inoperative. Maintenance has not inspected the aircraft yet; however there are signs of fire or extreme heat in the nose baggage area above the cabin heater. Smoke trails and burned paint. The reporter indicated that the fire appeared to be from residual cabin heater fuel that was ignited by a short in a wire bundle. The shorted wiring was also the source of the multiple electrical problems. The series of uncommanded movements in the roll axis is still under evaluation; but may have been wake turbulence. The aircraft has since been ferried to a nearby airport with no flight control issues reported. C414 pilot and flight instructor experienced several uncommanded wing rolling movements; possibly from wake turbulence; as well as electrical problems that resulted in a return to the field. After landing; smoke was observed in the cabin. Residual fuel from the cabin heater was reported to have been ignited by a shorted wire bundle which was likely also the source of the electrical problems.